Math Problem Statement

Write an equivalent expression without negative exponents​ and, if​ possible, simplify.

18 x Superscript negative 118x−1

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Part 1

Select the correct choice and fill in the answer​ box(es) to complete your choice.

​(Simplify your answer. Type exponential notation with positive exponents. Use integers or fractions for any numbers in the​ expression.)

A.

The expression

18 x Superscript negative 118x−1

expressed using positive exponents is

enter your response here.

This cannot be simplified further.

B.

The expression

18 x Superscript negative 118x−1

expressed using positive exponents is

enter your response here.

This can be simplified to

enter your response here.

Solution

Let's rewrite the given expression:

18x⁻¹

Step 1: Rewrite with Positive Exponents

To eliminate the negative exponent, recall that:

x1=1xx^{-1} = \frac{1}{x}

Thus,

18x1=18x18x^{-1} = \frac{18}{x}

Step 2: Check for Simplification

Since there's nothing else to factor or reduce, this is the simplest form.

Final Answer:

  • Choice A: The expression 18x118x^{-1} expressed using positive exponents is 18x\frac{18}{x}. This cannot be simplified further.

Would you like any further explanation on exponents or simplification steps?

Here are 5 related questions you might find useful:

  1. How do you simplify expressions with multiple negative exponents?
  2. What is the rule for multiplying terms with exponents?
  3. How do you simplify fractions with exponents in both the numerator and denominator?
  4. What happens when you raise a power to another power?
  5. How do you handle expressions with both negative and fractional exponents?

Tip: When dealing with negative exponents, remember they represent reciprocals!

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Math Problem Analysis

Mathematical Concepts

Algebra
Exponents
Negative Exponents

Formulas

x⁻¹ = 1/x

Theorems

Negative exponent rule

Suitable Grade Level

Grades 7-9